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Tagged with multivariable-calculus fourier-analysis
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Express Dirichlet energy $E_\mu(f) := \int \|\nabla f(x)\|^2 d\mu(x)$ in terms of Fourier information alone
Let $\mathbb R^d$ and let $\mu = p(dx)$ be a probability distribution thereupon, with density $p$ (which maybe assumed bounded, etc.). For a continuously differentiable function $f:\mathbb R^d \to \...
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